{"title":"Portmanteau tests for periodic ARMA models with dependent errors","authors":"Y. Boubacar Maïnassara, A. Ilmi Amir","doi":"10.1111/jtsa.12692","DOIUrl":null,"url":null,"abstract":"<p>In this article, we derive the asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations of (parsimonious) periodic autoregressive moving-average (PARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. We then deduce the modified portmanteau statistics. We establish the asymptotic behavior of the proposed statistics. It is shown that the asymptotic distribution of the modified portmanteau tests is that of a weighted sum of independent chi-squared random variables, which can be different from the usual chi-squared approximation used under independent and identically distributed assumption on the noise. We also propose another test based on a self-normalization approach to check the adequacy of PARMA models. A set of Monte Carlo experiments and an application to financial data are presented.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"45 2","pages":"164-188"},"PeriodicalIF":1.2000,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Time Series Analysis","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/jtsa.12692","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we derive the asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations of (parsimonious) periodic autoregressive moving-average (PARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. We then deduce the modified portmanteau statistics. We establish the asymptotic behavior of the proposed statistics. It is shown that the asymptotic distribution of the modified portmanteau tests is that of a weighted sum of independent chi-squared random variables, which can be different from the usual chi-squared approximation used under independent and identically distributed assumption on the noise. We also propose another test based on a self-normalization approach to check the adequacy of PARMA models. A set of Monte Carlo experiments and an application to financial data are presented.
期刊介绍:
During the last 30 years Time Series Analysis has become one of the most important and widely used branches of Mathematical Statistics. Its fields of application range from neurophysiology to astrophysics and it covers such well-known areas as economic forecasting, study of biological data, control systems, signal processing and communications and vibrations engineering.
The Journal of Time Series Analysis started in 1980, has since become the leading journal in its field, publishing papers on both fundamental theory and applications, as well as review papers dealing with recent advances in major areas of the subject and short communications on theoretical developments. The editorial board consists of many of the world''s leading experts in Time Series Analysis.